The empirical relation between solar radiation and hours of sunshine

The variation with latitude of the regression parameters a and b in the conventional equation of Ångström type\documentclass{article}\pagestyle{empty}\begin{document}$$ Q/Q_A = a + b\,n/N $$\end{document}between total solar radiation on a horizontal surface ( Q ) and hours of bright sunshine ( n ) has been examined. It has been shown that the slope of the relationship b is effectively constant, while the threshold value a is a function of latitude. An empirical relationship leading to the Ångström equation at each latitude ϕ over the range 0° ‐ 60° is derived and is shown to give values in reasonable accord with previous experience. It is\documentclass{article}\pagestyle{empty}\begin{document}$$ Q/Q_A = 2.09\,\cos \phi + 0.52\,\,n/N $$\end{document}